however, in mod 4, i have a^4 + 6(a^2)(b^2) + a^4
I've tried solving it out several ways, and I can't make mod 4 as pretty as the other mods. Why is this....? Am I doing the foil wrong? because I've tried it several ways to see if I was missing something, and almost thought i had it until i noticed I made a mistake and then got the result that is making it soooo not nice and neat as the others. Please help

however, in mod 4, i have a^4 + 6(a^2)(b^2) + a^4
I've tried solving it out several ways, and I can't make mod 4 as pretty as the other mods. Why is this....? Am I doing the foil wrong? because I've tried it several ways to see if I was missing something, and almost thought i had it until i noticed I made a mistake and then got the result that is making it soooo not nice and neat as the others. Please help

I can't solve your problem (I have an idea about prime n, so think about this case), but note that

I think the idea to concentrate on here is that the coefficient of each term is

point well taken, thanks! *chuckles* I guess i was hoping to have it nice and neat, but, I've learned long ago that its not as pretty as one would hope. But, just to make sure, if n is prime, it will be pretty right? but if its not prime.... then, each thing must be foiled out for itself, yes?